Question

Which of the following is greater than $1000.01$?
A).$0.00010001\times {10}^7$
B). $0.00001\times {10}^8$
C). $1.1\times {10}^2$
D). $1.00001\times {10}^3$

Answer 1

Hint: In the given problem, we have to find the greatest term which is greater than the given term. But here we have the decimal point terms. So we must understand and observe the decimal point and the power of ten. Using the given options is a very easy method to solve this problem.

Complete step-by-step solution:
In the given problem, we are going to find the greatest term which is greater than the given term $1000.01$
Using the given options we can solve this problem easily.
Or using another method we can solve this problem.
That is, make all the given terms in question and options have equal ten powers.
Now we are going to solve the problem in the first method. That solves all the given options.
And compare the solved option with the given term in the question.
First of all, the given term in the question is $1000.01$
Now we are going to simplify option A which is given
Therefore the option A is $0.00010001\times {10}^7$
In this term, after zero, we have eight numbers. And we have the seven to the power of seven.
Now multiply the term ten to the power of seven to the given number.
We get,
$=0.00010001\times 10\times 10\times 10\times 10\times 10\times 10\times 10$
$=0.00010001\times 10000000$
Now simplify this we get,
$=1000.1$ which is greater than the given number in the question.
This is the required solution for the given problem.
That is, $1000.1>1000.01$
Hence the solution for the given question is option A.
The explanation for the option B:
Option B is $0.00001\times {10}^8$.
 Now simplify this,
$0.00001\times 100000000$
Now we get,
$=1000$which is less than the given term.
$1000<1000.01$
Therefore option B is not an answer.
 The explanation for the option C:
Option C is $1.1\times {10}^2$
Now simplify this,
$1.1\times 100$
Now we get,
$=110$which is less than the given term in the question.
Therefore the option C is not an answer.
The explanation for the option D:
Option D is $1.00001\times {10}^3$
Now simplify this we get,
$$\begin{gathered} =1.00001\times 1000 \\ =1000.01 \end{gathered}$$
  Which is equal to the term given in the question.
Therefore option D is not an answer.

Note: Decimals are defined as the fraction that shows as a decimal point followed by the number of tenths, hundreds, thousands, etc., decimal comes from the Latin word Decimus. The word Decimus means tenth, from the root word Decem. In algebra, a decimal is defined as a number whose whole part and the fractional part and the fractional part are separated by the point.